A multifaceted study of marked Gibbs point processes

20.05.2021, 14:00
Forschungsseminar Wahrscheinlichkeitstheorie

Alexander Zass (UP)

In this talk we present some results on the existence and uniqueness of marked Gibbs point processes. Firstly, we prove in a general setting the existence of an infinite-volume marked Gibbs point process, via the so-called entropy method from large deviations theory. We then adapt it to the setting of infinite-dimen-sional Langevin diffusions, put in interaction via a Gibbsian description; we also obtain the uniqueness of such a Gibbs process via cluster expansion techniques. Finally, we explore the question of uniqueness in the case of repulsive interactions, in a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework.

Zoom-access is available on

www.math.uni-potsdam.de/fileadmin/user_upload/Prof-Wahr/Roelly/FS_21.pdf